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The cognitive mechanism by which Large Language Models (LLMs) solve mathematical problems remains a widely debated and unresolved issue. Currently, there is little interpretable experimental evidence that connects LLMs' problem-solving with human cognitive psychology.To determine if LLMs possess human-like mathematical reasoning, we modified the problems used in the human Cognitive Reflection Test (CRT). Our results show that, even with the use of Chains of Thought (CoT) prompts, mainstream LLMs, including the latest o1 model (noted for its reasoning capabilities), have a high error rate when solving these modified CRT problems. Specifically, the average accuracy rate dropped by up to 50% compared to the original questions.Further analysis of LLMs' incorrect answers suggests that they primarily rely on pattern matching from their training data, which aligns more with human intuition (System 1 thinking) rather than with human-like reasoning (System 2 thinking). This finding challenges the belief that LLMs have genuine mathematical reasoning abilities comparable to humans. As a result, this work may adjust overly optimistic views on LLMs' progress towards artificial general intelligence.

Spatio-temporal area-level datasets play a critical role in official statistics, providing valuable insights for policy-making and regional planning. Accurate modeling and forecasting of these datasets can be extremely useful for policymakers to develop informed strategies for future planning. Echo State Networks (ESNs) are efficient methods for capturing nonlinear temporal dynamics and generating forecasts. However, ESNs lack a direct mechanism to account for the neighborhood structure inherent in area-level data. Ignoring these spatial relationships can significantly compromise the accuracy and utility of forecasts. In this paper, we incorporate approximate graph spectral filters at the input stage of the ESN, thereby improving forecast accuracy while preserving the model's computational efficiency during training. We demonstrate the effectiveness of our approach using Eurostat's tourism occupancy dataset and show how it can support more informed decision-making in policy and planning contexts., Comment: 23 pages, 4 figures

With the ascent of large language models (LLM), natural language processing has witnessed enhancements, such as LLM-based data augmentation. Nonetheless, prior research harbors two primary concerns: firstly, a lack of contemplation regarding whether the natural language generated by LLM (LLMNL) truly aligns with human natural language (HNL), a critical foundational question; secondly, an oversight that augmented data is randomly generated by LLM, implying that not all data may possess equal training value, that could impede the performance of classifiers. To address these challenges, we introduce the scaling laws to intrinsically calculate LLMNL and HNL. Through extensive experiments, we reveal slight deviations (approximately 0.2 Mandelbrot exponent) from Mandelbrot's law in LLMNL, underscore a complexity advantage in HNL, and supplement an interpretive discussion on language style. This establishes a solid foundation for LLM's expansion. Further, we introduce a novel data augmentation method for few-shot text classification, termed ZGPTDA, which leverages fuzzy computing mechanisms driven by the conformity to scaling laws to make decisions about GPT-4 augmented data. Extensive experiments, conducted in real-world scenarios, confirms the effectiveness (improving F1 of Bert and RoBerta by 7-10%) and competitiveness (surpassing recent AugGPT and GENCO methods by about 2% accuracy on DeBerta) of ZGPTDA. In addition, we reveal some interesting insights, e.g., Hilberg's law and Taylor's law can impart more benefits to text classification, etc.

We study the policy iteration algorithm (PIA) for entropy-regularized stochastic control problems on an infinite time horizon with a large discount rate, focusing on two main scenarios. First, we analyze PIA with bounded coefficients where the controls applied to the diffusion term satisfy a smallness condition. We demonstrate the convergence of PIA based on a uniform $\mathcal{C}^{2,\alpha}$ estimate for the value sequence generated by PIA, and provide a quantitative convergence analysis for this scenario. Second, we investigate PIA with unbounded coefficients but no control over the diffusion term. In this scenario, we first provide the well-posedness of the exploratory Hamilton--Jacobi--Bellman equation with linear growth coefficients and polynomial growth reward function. By such a well-posedess result we achieve PIA's convergence by establishing a quantitative locally uniform $\mathcal{C}^{1,\alpha}$ estimates for the generated value sequence., Comment: 21 pages

Large Language Models (LLMs) have gradually become the gateway for people to acquire new knowledge. However, attackers can break the model's security protection ("jail") to access restricted information, which is called "jailbreaking." Previous studies have shown the weakness of current LLMs when confronted with such jailbreaking attacks. Nevertheless, comprehension of the intrinsic decision-making mechanism within the LLMs upon receipt of jailbreak prompts is noticeably lacking. Our research provides a psychological explanation of the jailbreak prompts. Drawing on cognitive consistency theory, we argue that the key to jailbreak is guiding the LLM to achieve cognitive coordination in an erroneous direction. Further, we propose an automatic black-box jailbreaking method based on the Foot-in-the-Door (FITD) technique. This method progressively induces the model to answer harmful questions via multi-step incremental prompts. We instantiated a prototype system to evaluate the jailbreaking effectiveness on 8 advanced LLMs, yielding an average success rate of 83.9%. This study builds a psychological perspective on the explanatory insights into the intrinsic decision-making logic of LLMs.

For time-inconsistent stopping in a one-dimensional diffusion setup, we investigate how to use discrete-time models to approximate the original problem. In particular, we consider the value function $V(\cdot)$ induced by all mild equilibria in the continuous-time problem, as well as the value $V^h(\cdot)$ associated with the equilibria in a binomial-tree setting with time step size $h$. We show that $\lim_{h\rightarrow 0+} V^h \leq V$. We provide an example showing that the exact convergence may fail. Then we relax the set of equilibria and consider the value $V^h_{\varepsilon}(\cdot)$ induced by $\varepsilon$-equilibria in the binomial-tree model. We prove that $\lim_{\varepsilon \rightarrow 0+}\lim_{h \rightarrow 0+}V^h_{\varepsilon} = V$.

We investigate an infinite-horizon time-inconsistent mean-field game (MFG) in a discrete time setting. We first present a classic equilibrium for the MFG and its associated existence result. This classic equilibrium aligns with the conventional equilibrium concept studied in MFG literature when the context is time-consistent. Then we demonstrate that while this equilibrium produces an approximate optimal strategy when applied to the related $N$-agent games, it does so solely in a precommitment sense. Therefore, it cannot function as a genuinely approximate equilibrium strategy from the perspective of a sophisticated agent within the $N$-agent game. To address this limitation, we propose a new consistent equilibrium concept in both the MFG and the $N$-agent game. We show that a consistent equilibrium in the MFG can indeed function as an approximate consistent equilibrium in the $N$-agent game. Additionally, we analyze the convergence of consistent equilibria for $N$-agent games toward a consistent MFG equilibrium as $N$ tends to infinity.

We initiate the study of Lie-Trotter means in JB-algebras, which is an extension of Lie-Trotter formulas in JB-algebras. We show that two-variable Lie-Trotter means include the weighted arithmetic mean, weighted harmonic mean, weighted geometric mean, and weighted spectral geometric mean. Consequently, several generalized Lie-Trotter formulas in JB-algebras are derived. Additionally, we demonstrate that the Sagae-Tanabe mean and Hansen's induction mean in JB-algebras are multivariable Lie-Trotter means. In the end, using arithmetic-geometric-harmonic mean inequalities we provide a characterization of multivariate Lie-Trotter means., Comment: 18 pages

The renowned proverb, Numbers do not lie, underscores the reliability and insight that lie beneath numbers, a concept of undisputed importance, especially in economics and finance etc. Despite the prosperity of Benford's Law in the first digit analysis, its scope fails to remain comprehensiveness when it comes to deciphering the laws of number. This paper delves into number laws by taking the financial statements of China real estate as a representative, quantitatively study not only the first digit, but also depict the other two dimensions of numbers: frequency and length. The research outcomes transcend mere reservations about data manipulation and open the door to discussions surrounding number diversity and the delineation of the usage insights. This study wields both economic significance and the capacity to foster a deeper comprehension of numerical phenomena., Comment: DSS

Textual geographic information is indispensable and heavily relied upon in practical applications. The absence of clear distribution poses challenges in effectively harnessing geographic information, thereby driving our quest for exploration. We contend that geographic information is influenced by human behavior, cognition, expression, and thought processes, and given our intuitive understanding of natural systems, we hypothesize its conformity to the Gamma distribution. Through rigorous experiments on a diverse range of 24 datasets encompassing different languages and types, we have substantiated this hypothesis, unearthing the underlying regularities governing the dimensions of quantity, length, and distance in geographic information. Furthermore, theoretical analyses and comparisons with Gaussian distributions and Zipf's law have refuted the contingency of these laws. Significantly, we have estimated the upper bounds of human utilization of geographic information, pointing towards the existence of uncharted territories. Also, we provide guidance in geographic information extraction. Hope we peer its true countenance uncovering the veil of geographic information., Comment: IPM

The renowned proverb that "The pen is mightier than the sword" underscores the formidable influence wielded by text expressions in shaping sentiments. Indeed, well-crafted written can deeply resonate within cultures, conveying profound sentiments. Nowadays, the omnipresence of the Internet has fostered a subculture that congregates around the contemporary milieu. The subculture artfully articulates the intricacies of human feelings by ardently pursuing the allure of novelty, a fact that cannot be disregarded in the sentiment analysis. This paper strives to enrich data through the lens of subculture, to address the insufficient training data faced by sentiment analysis. To this end, a new approach of subculture-based data augmentation (SCDA) is proposed, which engenders six enhanced texts for each training text by leveraging the creation of six diverse subculture expression generators. The extensive experiments attest to the effectiveness and potential of SCDA. The results also shed light on the phenomenon that disparate subculture expressions elicit varying degrees of sentiment stimulation. Moreover, an intriguing conjecture arises, suggesting the linear reversibility of certain subculture expressions. It is our fervent aspiration that this study serves as a catalyst in fostering heightened perceptiveness towards the tapestry of information, sentiment and culture, thereby enriching our collective understanding., Comment: JASIST

Large language models (LLMs), such as ChatGPT, have emerged with astonishing capabilities approaching artificial general intelligence. While providing convenience for various societal needs, LLMs have also lowered the cost of generating harmful content. Consequently, LLM developers have deployed semantic-level defenses to recognize and reject prompts that may lead to inappropriate content. Unfortunately, these defenses are not foolproof, and some attackers have crafted "jailbreak" prompts that temporarily hypnotize the LLM into forgetting content defense rules and answering any improper questions. To date, there is no clear explanation of the principles behind these semantic-level attacks and defenses in both industry and academia. This paper investigates the LLM jailbreak problem and proposes an automatic jailbreak method for the first time. We propose the concept of a semantic firewall and provide three technical implementation approaches. Inspired by the attack that penetrates traditional firewalls through reverse tunnels, we introduce a "self-deception" attack that can bypass the semantic firewall by inducing LLM to generate prompts that facilitate jailbreak. We generated a total of 2,520 attack payloads in six languages (English, Russian, French, Spanish, Chinese, and Arabic) across seven virtual scenarios, targeting the three most common types of violations: violence, hate, and pornography. The experiment was conducted on two models, namely the GPT-3.5-Turbo and GPT-4. The success rates on the two models were 86.2% and 67%, while the failure rates were 4.7% and 2.2%, respectively. This highlighted the effectiveness of the proposed attack method. All experimental code and raw data will be released as open-source to inspire future research. We believe that manipulating AI behavior through carefully crafted prompts will become an important research direction in the future., Comment: Serious errors were found in the experiment, which may lead to the overturning of the overall conclusions of the paper

The discrimination of instance embeddings plays a vital role in associating instances across time for online video instance segmentation (VIS). Instance embedding learning is directly supervised by the contrastive loss computed upon the contrastive items (CIs), which are sets of anchor/positive/negative embeddings. Recent online VIS methods leverage CIs sourced from one reference frame only, which we argue is insufficient for learning highly discriminative embeddings. Intuitively, a possible strategy to enhance CIs is replicating the inference phase during training. To this end, we propose a simple yet effective training strategy, called Consistent Training for Online VIS (CTVIS), which devotes to aligning the training and inference pipelines in terms of building CIs. Specifically, CTVIS constructs CIs by referring inference the momentum-averaged embedding and the memory bank storage mechanisms, and adding noise to the relevant embeddings. Such an extension allows a reliable comparison between embeddings of current instances and the stable representations of historical instances, thereby conferring an advantage in modeling VIS challenges such as occlusion, re-identification, and deformation. Empirically, CTVIS outstrips the SOTA VIS models by up to +5.0 points on three VIS benchmarks, including YTVIS19 (55.1% AP), YTVIS21 (50.1% AP) and OVIS (35.5% AP). Furthermore, we find that pseudo-videos transformed from images can train robust models surpassing fully-supervised ones., Comment: Accepted by ICCV 2023. The code is available at https://github.com/KainingYing/CTVIS

This paper considers an infinite-horizon Markov decision process (MDP) that allows for general non-exponential discount functions, in both discrete and continuous time. Due to the inherent time inconsistency, we look for a randomized equilibrium policy (i.e., relaxed equilibrium) in an intra-personal game between an agent's current and future selves. When we modify the MDP by entropy regularization, a relaxed equilibrium is shown to exist by a nontrivial entropy estimate. As the degree of regularization diminishes, the entropy-regularized MDPs approximate the original MDP, which gives the general existence of a relaxed equilibrium in the limit by weak convergence arguments. As opposed to prior studies that consider only deterministic policies, our existence of an equilibrium does not require any convexity (or concavity) of the controlled transition probabilities and reward function. Interestingly, this benefit of considering randomized policies is unique to the time-inconsistent case.

A comprehensive understanding of interested human-to-human interactions in video streams, such as queuing, handshaking, fighting and chasing, is of immense importance to the surveillance of public security in regions like campuses, squares and parks. Different from conventional human interaction recognition, which uses choreographed videos as inputs, neglects concurrent interactive groups, and performs detection and recognition in separate stages, we introduce a new task named human-to-human interaction detection (HID). HID devotes to detecting subjects, recognizing person-wise actions, and grouping people according to their interactive relations, in one model. First, based on the popular AVA dataset created for action detection, we establish a new HID benchmark, termed AVA-Interaction (AVA-I), by adding annotations on interactive relations in a frame-by-frame manner. AVA-I consists of 85,254 frames and 86,338 interactive groups, and each image includes up to 4 concurrent interactive groups. Second, we present a novel baseline approach SaMFormer for HID, containing a visual feature extractor, a split stage which leverages a Transformer-based model to decode action instances and interactive groups, and a merging stage which reconstructs the relationship between instances and groups. All SaMFormer components are jointly trained in an end-to-end manner. Extensive experiments on AVA-I validate the superiority of SaMFormer over representative methods. The dataset and code will be made public to encourage more follow-up studies.

In this note, we employ Jordan product within Banach algebras to present two error estimates of Lie-Trotter product formulas. Additionally, we introduce two generalized Lie-Trotter formula and provide two explicit estimation formulas. Consequently, the renowned Suzuki symmetrized approximation for the exponentiated sums follows directly from our Theorem 2.3. To conclude our paper, we offer a partial answer to a question concerning the Suzuki type estimations in Jordan-Banach algebras., Comment: 8 pages

Lie-Trotter-Suzuki product formulas are ubiquitous in quantum mechanics, computing, and simulations. Approximating exponentiated sums with Jordan product formulas are investigated in the setting of JB-algebras. We show that the Suzuki type approximation for exponentiated sums holds in JB-algebras, we give explicit estimation formulas, and we deduce three generalizations of Lie-Trotter formulas for arbitrary number elements in such algebras. We also extended the Lie-Trotter formulas in a Jordan Banach algebra from three elements to an arbitrary number of elements., Comment: 12 pages

Monocular depth estimation has been actively studied in fields such as robot vision, autonomous driving, and 3D scene understanding. Given a sequence of color images, unsupervised learning methods based on the framework of Structure-From-Motion (SfM) simultaneously predict depth and camera relative pose. However, dynamically moving objects in the scene violate the static world assumption, resulting in inaccurate depths of dynamic objects. In this work, we propose a new method to address such dynamic object movements through monocular 3D object detection. Specifically, we first detect 3D objects in the images and build the per-pixel correspondence of the dynamic pixels with the detected object pose while leaving the static pixels corresponding to the rigid background to be modeled with camera motion. In this way, the depth of every pixel can be learned via a meaningful geometry model. Besides, objects are detected as cuboids with absolute scale, which is used to eliminate the scale ambiguity problem inherent in monocular vision. Experiments on the KITTI depth dataset show that our method achieves State-of-The-Art performance for depth estimation. Furthermore, joint training of depth, camera motion and object pose also improves monocular 3D object detection performance. To the best of our knowledge, this is the first work that allows a monocular 3D object detection network to be fine-tuned in a self-supervised manner.

For a general entropy-regularized stochastic control problem on an infinite horizon, we prove that a policy iteration algorithm (PIA) converges to an optimal relaxed control. Contrary to the standard stochastic control literature, classical H\"{o}lder estimates of value functions do not ensure the convergence of the PIA, due to the added entropy-regularizing term. To circumvent this, we carry out a delicate estimation by moving back and forth between appropriate H\"{o}lder and Sobolev spaces. This requires new Sobolev estimates designed specifically for the purpose of policy iteration and a nontrivial technique to contain the entropy growth. Ultimately, we obtain a uniform H\"{o}lder bound for the sequence of value functions generated by the PIA, thereby achieving the desired convergence result. Characterization of the optimal value function as the unique solution to an exploratory Hamilton-Jacobi-Bellman equation comes as a by-product. The PIA is numerically implemented in an example of optimal consumption.

Hazard and operability analysis (HAZOP) is the paradigm of industrial safety that can reveal the hazards of process from its node deviations, consequences, causes, measures and suggestions, and such hazards can be considered as hazard events (HaE). The classification research on HaE has much irreplaceable pragmatic values. In this paper, we present a novel deep learning model termed DLF through multifractal to explore HaE classification where the motivation is that HaE can be naturally regarded as a kind of time series. Specifically, first HaE is vectorized to get HaE time series by employing BERT. Then, a new multifractal analysis method termed HmF-DFA is proposed to win HaE fractal series by analyzing HaE time series. Finally, a new hierarchical gating neural network (HGNN) is designed to process HaE fractal series to accomplish the classification of HaE from three aspects: severity, possibility and risk. We take HAZOP reports of 18 processes as cases, and launch the experiments on this basis. Results demonstrate that compared with other classifiers, DLF classifier performs better under metrics of precision, recall and F1-score, especially for the severity aspect. Also, HmF-DFA and HGNN effectively promote HaE classification. Our HaE classification system can serve application incentives to experts, engineers, employees, and other enterprises. We hope our research can contribute added support to the daily practice in industrial safety., Comment: accepted by Computers In Industry

We demonstrate a robust low-loss optical interface by tiling passive (i.e., without doping of active ions) thin film lithium niobate (TFLN) and active (i.e., doped with rare earth ions) TFLN substrates for monolithic integration of passive/active lithium niobate photonics. The tiled substrates composed of both active and passive areas allow to pattern the mask of the integrated active passive photonic device at once using a single continuous photolithography process. The interface loss of tiled substrate is measured as low as 0.26 dB. Thanks to the stability provided by this approach, a four-channel waveguide amplifier is realized in a straightforward manner, which shows a net gain of ~5 dB at 1550-nm wavelength and that of ~8 dB at 1530-nm wavelength for each channel. The robust low-loss optical interface for passive/active photonic integration will facilitate large-scale high performance photonic devices which require on-chip light sources and amplifiers., Comment: 13 pages, 5 figures